What is the integral of 4x-6xy^2-2 ?

The integral of 4x-6xy^2-2 is -2x+2x^2-3y^2x^2+C

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integral of 4x-6xy^2-2

\int 4 x - 6 x y^{2} - 2 d x

- 2 x + 2 x^{2} - 3 y^{2} x^{2} + C

Solution steps

\int 4 x - 6 x y^{2} - 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 2 d x + \int 4 x d x - \int 6 y^{2} x d x

\int 2 d x = 2 x

\int 4 x d x = 2 x^{2}

\int 6 y^{2} x d x = 3 y^{2} x^{2}

= - 2 x + 2 x^{2} - 3 y^{2} x^{2}

Add a constant to the solution

= - 2 x + 2 x^{2} - 3 y^{2} x^{2} + C

What is the integral of 4x-6xy^2-2 ?
The integral of 4x-6xy^2-2 is -2x+2x^2-3y^2x^2+C